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A Learning Search Algorithm for the Restricted Longest Common Subsequence Problem

Marko Djukanović, Jaume Reixach, Ana Nikolikj, Tome Eftimov, Aleksandar Kartelj, Christian Blum

TL;DR

Two novel heuristic approaches designed to enhance the search process by steering it towards promising regions in the search space are introduced, one based on a neural network model trained offline using a genetic algorithm and another based on a neural network model trained offline using a genetic algorithm.

Abstract

This paper addresses the Restricted Longest Common Subsequence (RLCS) problem, an extension of the well-known Longest Common Subsequence (LCS) problem. This problem has significant applications in bioinformatics, particularly for identifying similarities and discovering mutual patterns and important motifs among DNA, RNA, and protein sequences. Building on recent advancements in solving this problem through a general search framework, this paper introduces two novel heuristic approaches designed to enhance the search process by steering it towards promising regions in the search space. The first heuristic employs a probabilistic model to evaluate partial solutions during the search process. The second heuristic is based on a neural network model trained offline using a genetic algorithm. A key aspect of this approach is extracting problem-specific features of partial solutions and the complete problem instance. An effective hybrid method, referred to as the learning beam search, is developed by combining the trained neural network model with a beam search framework. An important contribution of this paper is found in the generation of real-world instances where scientific abstracts serve as input strings, and a set of frequently occurring academic words from the literature are used as restricted patterns. Comprehensive experimental evaluations demonstrate the effectiveness of the proposed approaches in solving the RLCS problem. Finally, an empirical explainability analysis is applied to the obtained results. In this way, key feature combinations and their respective contributions to the success or failure of the algorithms across different problem types are identified.

A Learning Search Algorithm for the Restricted Longest Common Subsequence Problem

TL;DR

Two novel heuristic approaches designed to enhance the search process by steering it towards promising regions in the search space are introduced, one based on a neural network model trained offline using a genetic algorithm and another based on a neural network model trained offline using a genetic algorithm.

Abstract

This paper addresses the Restricted Longest Common Subsequence (RLCS) problem, an extension of the well-known Longest Common Subsequence (LCS) problem. This problem has significant applications in bioinformatics, particularly for identifying similarities and discovering mutual patterns and important motifs among DNA, RNA, and protein sequences. Building on recent advancements in solving this problem through a general search framework, this paper introduces two novel heuristic approaches designed to enhance the search process by steering it towards promising regions in the search space. The first heuristic employs a probabilistic model to evaluate partial solutions during the search process. The second heuristic is based on a neural network model trained offline using a genetic algorithm. A key aspect of this approach is extracting problem-specific features of partial solutions and the complete problem instance. An effective hybrid method, referred to as the learning beam search, is developed by combining the trained neural network model with a beam search framework. An important contribution of this paper is found in the generation of real-world instances where scientific abstracts serve as input strings, and a set of frequently occurring academic words from the literature are used as restricted patterns. Comprehensive experimental evaluations demonstrate the effectiveness of the proposed approaches in solving the RLCS problem. Finally, an empirical explainability analysis is applied to the obtained results. In this way, key feature combinations and their respective contributions to the success or failure of the algorithms across different problem types are identified.

Paper Structure

This paper contains 24 sections, 11 equations, 12 figures, 13 tables, 3 algorithms.

Table of Contents

  1. Introduction
  2. Preliminaries
  3. Search Approaches for the RLCS Problem
  4. The General Search Scheme
  5. A$^*$ Search Algorithm
  6. Beam Search Algorithm
  7. Upper bounds
  8. A Probability-based Heuristic Function for RLCS
  9. Learning Beam Search Approach
  10. Features
  11. Node features
  12. Instance features
  13. Neural Network Training
  14. Experimental Evaluation
  15. Problem instances
  16. ...and 9 more sections

Figures (12)

  • Figure 1: Example of the full state graph in the form of a directed acyclic graph for the problem instance $(S=\{s_1=\texttt{TCAACTGT}, s_2=\texttt{CTCCACGT}\},\ R=\{r_1=\texttt{CTT}, r_2=\texttt{TA}\}$). It contains eight complete nodes (light grey background). The two paths from $((9, 9), (3, 2), 5)$ to the root node (in blue) are the longest paths in the graph. Hence, they represent two optimal solutions for this problem instance, i.e., $\texttt{TCCGT}$ and $\texttt{CACGT}$, respectively.
  • Figure 2: A graphical representation of the feed-forward neural network employed for benchmark set Abstract. The lines from the top node in each layer represent the biases. Remember that two extra instance features are considered in the context of benchmark set Random, as opposed to the benchmark set Abstract.
  • Figure 3: Comparisons of the three BS variants regarding different $\beta$ values on the Random benchmark set
  • Figure 4: BS-ub: results for different $\beta$ values on benchmark set Abstract
  • Figure 5: BS-prob: results for different $\beta$ values on benchmark set Abstract
  • ...and 7 more figures